A minimal physics-based model for musical perception.

Some people, entirely untrained in music, can listen to a song and replicate it on a piano with unnerving accuracy. What enables some to "hear" music so much better than others? Long-standing research confirms that part of the answer is undoubtedly neurological and can be improved with training. However, are there structural, physical, or engineering attributes of the human hearing mechanism apparatus (i.e., the hair cells of the internal ear) that render one human innately superior to another in terms of propensity to listen to music? In this work, we investigate a physics-based model of the electromechanics of the hair cells in the inner ear to understand why a person might be physiologically better poised to distinguish musical sounds. A key feature of the model is that we avoid a "black-box" systems-type approach. All parameters are well-defined physical quantities, including membrane thickness, bending modulus, electromechanical properties, and geometrical features, among others. Using the two-tone interference problem as a proxy for musical perception, our model allows us to establish the basis for exploring the effect of external factors such as medicine or environment. As an example of the insights we obtain, we conclude that the reduction in bending modulus of the cell membranes (which for instance may be caused by the usage of a certain class of analgesic drugs) or an increase in the flexoelectricity of the hair cell membrane can interfere with the perception of two-tone excitation.

The giant flexoelectric effect in a luffa plant-based sponge for green devices and energy harvesters.

Soft materials that can produce electrical energy under mechanical stimulus or deform significantly via moderate electrical fields are important for applications ranging from soft robotics to biomedical science. Piezoelectricity, the property that would ostensibly promise such a realization, is notably absent from typical soft matter. Flexoelectricity is an alternative form of electromechanical coupling that universally exists in all dielectrics and can generate electricity under nonuniform deformation such as flexure and conversely, a deformation under inhomogeneous electrical fields. The flexoelectric coupling effect is, however, rather modest for most materials and thus remains a critical bottleneck. In this work, we argue that a significant emergent flexoelectric response can be obtained by leveraging a hierarchical porous structure found in biological materials. We experimentally illustrate our thesis for a natural dry luffa vegetable-based sponge and demonstrate an extraordinarily large mass- and deformability-specific electromechanical response with the highest-density-specific equivalent piezoelectric coefficient known for any material (50 times that of polyvinylidene fluoride and more than 10 times that of lead zirconate titanate). Finally, we demonstrate the application of the fabricated natural sponge as green, biodegradable flexible smart devices in the context of sensing (e.g., for speech, touch pressure) and electrical energy harvesting.

Flexoelectric Enhancement of Strain Gradient Elasticity Across a Ferroelectric-to-Paraelectric Phase Transition.

We study the temperature dependent elastic properties of Ba0.8Sr0.2TiO3 freestanding membranes across the ferroelectric-to-paraelectric phase transition using an atomic force microscope. The bending rigidity of thin membranes can be stiffer compared to stretching due to strain gradient elasticity (SGE). We measure the Young's modulus of freestanding Ba0.8Sr0.2TiO3 drumheads in bending and stretching dominated deformation regimes on a variable temperature platform, finding a peak in the difference between the two Young's moduli obtained at the phase transition. This demonstrates a dependence of SGE on the dielectric properties of a material and alludes to a flexoelectric origin of an effective SGE.

Enhanced Electromechanical Response Due to Inhomogeneous Strain in Monolayer MoS2.

2D transition metal dichalcogenides (TMDs) exhibit exceptional resilience to mechanical deformation. Applied strain can have pronounced effects on properties such as the bandgaps and exciton dynamics of TMDs, via deformation potentials and electromechanical coupling. In this work, we use piezoresponse force microscopy to show that the inhomogeneous strain from nanobubbles produces dramatic, localized enhancements of the electromechanical response of monolayer MoS2. Nanobubbles with diameters under 100 nm consistently produce an increased piezoresponse that follows the features' topography, while larger bubbles exhibit a halo-like profile, with maximum piezoresponse near the periphery. We show that spatial filtering enables these effects to be eliminated in the quantitative determination of effective piezoelectric or flexoelectric coefficients. Numerical strain modeling reveals a correlation between the hydrostatic strain gradient and the effective piezoelectric coefficient in large MoS2 nanobubbles, suggesting a localized variation in electromechanical coupling due to symmetry reduction induced by inhomogeneous strain.

Giant Flexoelectricity in Bent Semiconductor Thinfilm.

We elucidate the flexoelectricity of semiconductors in the high strain gradient regime, the underlying mechanism of which is less understood. By using the generalized Bloch theorem, we uncover a strong flexoelectric-like effect in bent thinfilms of Si and Ge due to a high-strain-gradient-induced band gap closure. We show that an unusual type-II band alignment is formed between the compressed and elongated sides of the bent film. Therefore, upon the band gap closure, electrons transfer from the compressed side to the elongated side to reach the thermodynamic equilibrium, leading to a pronounced change of polarization along the film thickness dimension. The obtained transverse flexoelectric coefficients are unexpectedly high with a quadratic dependence on the film thickness. This new mechanism is extendable to other semiconductor materials with moderate energy gaps. Our findings have important implications for the future applications of flexoelectricity in semiconductor materials.

Flexoelectricity, Triboelectricity, and Free Interfacial Charges.

Triboelectricity has been a topic of some confusion for many years, probably because it is very diverse and some of the fundamental science has not been clear. This is now starting to change. A few years ago, the importance of flexoelectricity at asperities is pointed out. That paper exploited the established physics of compensation of bound surface or interfacial charges without going into detail. The purpose of this paper is to expand further on this, mapping from the established physics of electrostatics with contact potentials and Maxwell's displacement field to the underlying fundamentals of charge transfer in triboelectricity. Examples from the published literature are used to illustrate this. In the discussion, some of the open questions and challenges to the community are mentioned.

Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity.

Soft robotics requires materials that are capable of large deformation and amenable to actuation with external stimuli such as electric fields. Energy harvesting, biomedical devices, flexible electronics, and sensors are some other applications enabled by electroactive soft materials. The phenomenon of flexoelectricity is an enticing alternative that refers to the development of electric polarization in dielectrics when subjected to strain gradients. In particular, flexoelectricity offers a direct linear coupling between a highly desirable deformation mode (flexure) and electric stimulus. Unfortunately, barring some exceptions, the flexoelectric effect is quite weak and rather substantial bending curvatures are required for an appreciable electromechanical response. Most experiments in the literature appear to confirm modest flexoelectricity in polymers although perplexingly, a singular work has measured a "giant" effect in elastomers under some specific conditions. Due to the lack of an understanding of the microscopic underpinnings of flexoelectricity in elastomers and a commensurate theory, it is not currently possible to either explain the contradictory experimental results on elastomers or pursue avenues for possible design of large flexoelectricity. In this work, we present a statistical-mechanics theory for the emergent flexoelectricity of elastomers consisting of polar monomers. The theory is shown to be valid in broad generality and leads to key insights regarding both giant flexoelectricity and material design. In particular, the theory shows that, in standard elastomer networks, combining stretching and bending is a mechanism for obtaining giant flexoelectricity, which also explains the aforementioned, surprising experimental discovery.

Flexo-/Piezoelectric Polarization Boosting Exciton Dissociation in Curved Two-Dimensional Carbon Nitride Photocatalyst.

Two-dimensional (2D) carbon nitride (CN) materials have received tremendous attention as photocatalysts for clean energy and environmental treatment. However, the photocatalytic efficiency of CN is constrained by the high exciton binding energy and sluggish charge kinetics due to weak dielectric screening, impeding the overall process. Herein, localized flexo-/piezoelectric polarization is introduced via strain engineering, boosting exciton dissociation and promoting charge separation to enhance the multielectron photocatalytic process. Consequently, the exciton binding energy of polarized CN is reduced from 52 to 34 meV, and the hydrogen evolution yield increased by 2.9 times compared to that of the pristine CN. For other photocatalytic reactions (e.g., H2O2 production), the polarized CN also maintained a 2.1-fold increase compared to the pristine CN. This strategy of inducing localized polarization via strain engineering provides new insights for boosting photocatalytic reactions involving electrons.

Spatial Tuning of Light-Matter Interaction via Strain-Gradient-Induced Polarization in Freestanding Wrinkled 2D Materials.

To date, controlled deformation of two-dimensional (2D) materials has been extensively demonstrated with substrate-supported structures. However, interfacial effects arising from these supporting materials may suppress or alter the unique behavior of the deformed 2D materials. To address interfacial effects, we report, for the first time, the formation of a micrometer-scale freestanding wrinkled structure of 2D material without any encapsulation layers where we observed the enhanced light-matter interactions with a spatial modulation. Freestanding wrinkled monolayer WSe2 exhibited about a 330% enhancement relative to supported wrinkled WSe2 quantified through photoinduced force microscopy. Spatial modulation and enhancement of light interaction in the freestanding wrinkled structures are attributed to the enhanced strain-gradient effect (i.e., out-of-plane polarization) enabled by removing the constraining support and proximate dielectrics. Our findings offer an additional degree of freedom to modulate the out-of-plane polarization and enhance the out-of-plane light-matter interaction in 2D materials.

Directly Observing the Evolution of Flexoelectricity at the Tip of Nanocracks.

As an electromechanical coupling between strain gradients and polarization, flexoelectricity is largely enhanced at the nanoscale. However, directly observing the evolution of flexoelectric fields at the nanoscale usually suffers from the difficulty of producing strain gradients and probing electrical responses simultaneously. Here, we introduce nanocracks in SrTiO3, Ba0.67Sr0.33TiO3, and TiO2 samples and apply continuously varying mechanical loading to them, and as a result, huge strain gradients appear at the crack tip and result in a significant flexoelectric effect. Then, using atomic force microscopy, we successfully measure the evolution of flexoelectricity around the crack tips. For the case of SrTiO3, the maximum induced electric field reaches 11 kV/m due to the tensile load increasing. The proposed method provides a reliable way to identify the significance of the flexoelectric effect. It may also open a new avenue for the study of flexoelectricity involving multiple physics phenomena including flexoelectronics, the flexo-photovoltaic effect, and others.

Tip-Induced In-Plane Ferroelectric Superstructure in Zigzag-Wrinkled BaTiO3 Thin Films.

The complex micro-/nanoscale wrinkle morphology primarily fabricated by elastic polymers is usually designed to realize unique functionalities in physiological, biochemical, bioelectric, and optoelectronic systems. In this work, we fabricated inorganic freestanding BaTiO3 ferroelectric thin films with zigzag wrinkle morphology and successfully modulated the ferroelectric domains to form an in-plane (IP) superstructure with periodic surface charge distribution. Our piezoresponse force microscopy (PFM) measurements and phase-field simulation demonstrate that the self-organized strain/stress field in the zigzag-wrinkled BaTiO3 film generates a corresponding pristine domain structure. These domains can be switched by tip-induced strain gradient (flexoelectricity) and naturally form a robust and unique "braided" in-plane domain pattern, which enables us to offer an effective and convenient way to create a microscopic ferroelectric superstructure. The corresponding periodic surface potential distribution provides an extra degree of freedom in addition to the morphology that could regulate cells or polar molecules in physiological and bioelectric applications.

Band Bending and Ratcheting Explain Triboelectricity in a Flexoelectric Contact Diode.

Triboelectricity was recognized millennia ago, but the fundamental mechanism of charge transfer is still not understood. We have recently proposed a model where flexoelectric band bending due to local asperity contacts drives triboelectric charge transfer in non-metals. While this ab initio model is consistent with a wide range of observed phenomena, to date there have been no quantitative analyses of the proposed band bending. In this work we use a Pt0.8Ir0.2 conductive atomic force microscope probe to simultaneously deform a Nb-doped SrTiO3 sample and collect current-bias data. The current that one expects based upon an analysis including the relevant flexoelectric band bending for a deformed semiconductor quantitively agrees with the experiments. The analysis indicates a general ratcheting mechanism for triboelectric transfer and strong experimental evidence that flexoelectric band bending is of fundamental importance for triboelectric contacts.

When Flexoelectricity Drives Triboelectricity.

Triboelectricity has been known since antiquity, but the fundamental science underlying this phenomenon lacks consensus. We present a flexoelectric model for triboelectricity where contact deformation induced band bending at the nanoscale is the driving force for charge transfer. This framework is combined with first-principles and finite element calculations to explore charge transfer implications for different contact geometry and materials combinations. We demonstrate that our ab initio based formulation is compatible with existing empirical models and experimental observations including charge transfer between similar materials and size/pressure dependencies associated with triboelectricity.

Mechanical Polarization Switching in Hf0.5Zr0.5O2 Thin Film.

HfO2-based films with high compatibility with Si and complementary metal-oxide semiconductors (CMOS) have been widely explored in recent years. In addition to ferroelectricity and antiferroelectricity, flexoelectricity, the coupling between polarization and a strain gradient, is rarely reported in HfO2-based films. Here, we demonstrate that the mechanically written out-of-plane domains are obtained in 10 nm Hf0.5Zr0.5O2 (HZO) ferroelectric film at room temperature by generating the stress gradient via the tip of an atomic force microscope. The results of scanning Kelvin force microscopy (SKPM) exclude the possibility of flexoelectric-like mechanisms and prove that charge injection could be avoided by mechanical writing and thus reveal the true polarization state, promoting wider flexoelectric applications and ultrahigh-density storage of HZO thin films.

Hexagonal Network of Photocurrent Enhancement in Few-Layer Graphene/InGaN Quantum Dot Junctions.

Strain in two-dimensional (2D) materials has attracted particular attention because of the remarkable modification of electronic and optical properties. However, emergent electromechanical phenomena and hidden mechanisms, such as strain-superlattice-induced topological states or flexoelectricity under strain gradient, remain under debate. Here, using scanning photocurrent microscopy, we observe significant photocurrent enhancement in hybrid vertical junction devices made of strained few-layer graphene and InGaN quantum dots. Optoelectronic response and photoluminescence measurements demonstrate a possible mechanism closely tied to the flexoelectric effect in few-layer graphene, where the strain can induce a lateral built-in electric field and assist the separation of electron-hole pairs. Photocurrent mapping reveals an unprecedentedly ordered hexagonal network, suggesting the potential to create a superlattice by strain engineering. Our work provides insights into optoelectronic phenomena in the presence of strain and paves the way for practical applications associated with strained 2D materials.

Large-Scale Domain Engineering in Two-Dimensional Ferroelectric CuInP2S6 via Giant Flexoelectric Effect.

Room-temperature ferroelectricity in two-dimensional (2D) materials is a potential for developing atomic-scale functional devices. However, as a key step for the technology implementations of 2D ferroelectrics in electronics, the controllable generation of uniform domains remains challenging at the current stage because domain engineering through an external electric field at the 2D limit inevitably leads to large leakage currents and material breakdown. Here, we demonstrate a voltage-free method, the flexoelectric effect, to artificially generate large-scale stripe domains in 2D ferroelectric CuInP2S6 with single domain lateral size at the scale of several hundred microns. With giant strain gradients (∼106 m-1), we mechanically switch the out-of-plane polarization in ultrathin CuInP2S6. The flexoelectric control of polarization is understood with a distorted Landau-Ginzburg-Devonshire double well model. Through substrate strain engineering, the stripe domain density is controllable. Our results highlight the potential of developing van der Waals ferroelectrics-based flexible electronics.

Mechanical Stress Modulation of Resistance in MoS2 Junctions.

Strain engineering is a powerful strategy to control the physical properties of material-enabling devices with enhanced functionality and improved performance. Here, we investigate a modulation of the transport behavior of the two-dimensional MoS2 junctions under the mechanical stress induced by a tip of an atomic force microscope (AFM). We show that the junction resistance can be reversibly tuned by up to 4 orders of magnitude by altering a tip-induced force. Analysis of the stress-induced evolution of the I-V characteristics indicates a combined effect of the tip-induced strain and strain gradient on the energy barrier height and profile. In addition, we show that the tip-generated flexoelectric effect leads to significant enhancement of the photovoltaic effect in the MoS2 junctions. A combination of the optical and mechanical stimuli facilitates reversible photomechanical tuning of resistance of the narrow-band 2D semiconductors and development of devices with an enhanced photovoltaic response.

Polymer Electrolytes as Energy-Harvesting Materials to Capture Electrical Energy from Dynamic Mechanical Deformations.

Ionic electroactive polymers (iEAPs) can generate electrical energy under bending deformations exhibiting great potential for fabricating energy harvesters from dynamic vibrating environments. According to a previous study, this flexoelectric energy-harvesting potential is explored in polymer electrolyte membrane (PEM) assemblies subjected to intermittent square wave bending modes. The above study reveals that the mechanoelectrical transduction is likely to be the consequence of ion polarization under a pressure gradient across the PEM thickness. To further evaluate the applicability of the PEM assemblies for harvesting energy from dynamic environments, oscillatory bending deformation is applied in the present study, whereby the complex flexoelectric coefficient corresponding to dynamic capacitance exhibits strong frequency dependence. At very high oscillatory bending frequencies, the ionic clouds inside the PEM assemblies cannot be fully polarized, and thus the corresponding energy output tends to become smaller. However, the PEM assemblies having higher ionic conductivities can enhance energy output at high frequencies. Of particular interest is that the incorporated ionic liquid (IL) is not only capable of effectively plasticizing the polymer network, but also expediting the ionic conductivity, thereby enhancing the electrical energy output, which in turn provides important design guidance for efficient polymer energy harvesters.

Fluid pumping and active flexoelectricity can promote lumen nucleation in cell assemblies.

We discuss the physical mechanisms that promote or suppress the nucleation of a fluid-filled lumen inside a cell assembly or a tissue. We discuss lumen formation in a continuum theory of tissue material properties in which the tissue is described as a 2-fluid system to account for its permeation by the interstitial fluid, and we include fluid pumping as well as active electric effects. Considering a spherical geometry and a polarized tissue, our work shows that fluid pumping and tissue flexoelectricity play a crucial role in lumen formation. We furthermore explore the large variety of long-time states that are accessible for the cell aggregate and its lumen. Our work reveals a role of the coupling of mechanical, electrical, and hydraulic phenomena in tissue lumen formation.

Strain Gradient Elasticity in SrTiO3 Membranes: Bending versus Stretching.

Young's modulus determines the mechanical loads required to elastically stretch a material and also the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. The associated energy cost can additionally contribute to elasticity via strain gradients, particularly at small length scales where they are geometrically enhanced. Here, we present nanomechanical measurements of freely suspended SrTiO3 crystalline membrane drumheads. We observe an unexpected nonmonotonic thickness dependence of Young's modulus upon small deflections. Furthermore, the modulus inferred from a predominantly bending deformation is three times larger than that of a predominantly stretching deformation for membranes thinner than 20 nm. In this regime we extract a strain gradient elastic coupling of ∼2.2 µN, which could be used in new operational regimes of nanoelectro-mechanics.